Bounded rationality for relaxing best response and mutual consistency: The Quantal Hierarchy model of decision-making

While game theory has been transformative for decision-making, the assumptions made can be overly restrictive in certain instances. In this work, we focus on some of the assumptions underlying rationality, such as mutual consistency and best response, and consider ways to relax these assumptions using concepts from level-$k$ reasoning and quantal response equilibrium (QRE) respectively. Specifically, we propose an information-theoretic two-parameter model that can relax both mutual consistency and best response, while still recovering approximations of level-$k$, QRE, or typical Nash equilibrium behaviour in the limiting cases. The proposed Quantal Hierarchy model is based on a recursive form of the variational free energy principle, representing higher-order reasoning as (pseudo) sequential decisions. Bounds in player processing abilities are captured as information costs, where future chains of reasoning in an extensive-form game tree are discounted, implying a hierarchy of players where lower-level players have fewer processing resources. We demonstrate the applicability of the proposed model to several canonical economic games.